Department of

# Mathematics

Seminar Calendar
for Graduate Geometry/Topology Seminar events the year of Thursday, September 14, 2017.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2017           September 2017          October 2017
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5                   1  2    1  2  3  4  5  6  7
6  7  8  9 10 11 12    3  4  5  6  7  8  9    8  9 10 11 12 13 14
13 14 15 16 17 18 19   10 11 12 13 14 15 16   15 16 17 18 19 20 21
20 21 22 23 24 25 26   17 18 19 20 21 22 23   22 23 24 25 26 27 28
27 28 29 30 31         24 25 26 27 28 29 30   29 30 31



Friday, January 20, 2017

4:00 pm in 241 Altgeld Hall,Friday, January 20, 2017

#### Organizational Meeting

Abstract: This is the organizational meeting to get the schedule of talks down for the spring. If you think you might be interested in giving a talk at some point, please attend!

Friday, January 27, 2017

4:00 pm in 241 Altgeld Hall,Friday, January 27, 2017

#### Galois Categories and the Topological Galois Correspondence

###### Daniel Carmody (UIUC Math)

Abstract: Classical Galois theory for fields gives a correspondence between closed subgroups of the Galois group of a Galois extension and intermediate subfields. The theory of covering spaces in topology gives a correspondence between connected coverings of nice spaces and subgroups of the fundamental group. The purpose of this talk is to explain the relationship between (and generalization) of these two theorems.

Friday, February 3, 2017

4:00 pm in 241 Altgeld Hall,Friday, February 3, 2017

#### Train Tracks on Surfaces

###### Marissa Loving (UIUC Math)

Abstract: Our mantra throughout the talk will be simple, "Train tracks approximate simple closed curves." Our goal will be to explore some examples of train tracks, draw some meaningful pictures, and develop an analogy between train tracks and another well known method of approximation. No great knowledge of anything is required for this talk as long as one is willing to squint their eyes at the blackboard a bit at times.

Friday, February 10, 2017

4:00 pm in 241 Altgeld Hall,Friday, February 10, 2017

#### Opers and non-abelian Hodge theory

###### Georgios Kydonakis (UIUC Math)

Abstract: We will describe two different families of flat $G$-connections over a compact Riemann surface for a complex, simple, simply connected Lie group $G$. The first is the family of $G$-opers, which for $G=\text{SL(2}\text{,}\mathbb{C}\text{)}$ can be thought of as global versions of the locally defined second order Schrödinger operators. The second comes from a particular subfamily of solutions to the so-called $G$-Hitchin equations. The physicist Davide Gaiotto conjectured that for $G=\text{SL(}n\text{,}\mathbb{C}\text{)}$ the second family in a scaling limit converges to a limiting connection which has the structure of an oper. We will describe a proof of this conjecture. This is joint work with Olivia Dumitrescu, Laura Fredrickson, Rafe Mazzeo, Motohico Mulase and Andrew Neitzke.

Friday, February 17, 2017

4:00 pm in 241 Altgeld Hall,Friday, February 17, 2017

#### Hyperbolic taxi cabs and conic kitty cats: a mathematical activity and coloring book

###### Melinda Lanius (UIUC Math)

Abstract: In this extremely interactive talk, we will develop intuition for various metrics that I have encountered in my own research. We’ll work our way through understanding more familiar spaces such as the real plane as well as hyperbolic plane and disk, to less familiar objects: such as a surface with a Euclidean, cylindrical, or hyperbolic-funnel end. Some markers and colored pencils will be provided, but please feel free to bring your own fun office supplies.

Friday, February 24, 2017

4:00 pm in 241 Altgeld Hall,Friday, February 24, 2017

#### Geometry of convex hypersurfaces

###### Bill Karr (UIUC Math)

Abstract: A convex hypersurface in Euclidean space or Minkowski space is the boundary of an open convex set. Smooth convex hypersurfaces have non-negative sectional curvature and indicate properties of more general Riemannian manifolds with non-negative curvature. I will discuss some properties of convex hypersurfaces. Finally, I will describe a problem that arises from Lorentzian geometry involving convex hypersurfaces and geodesic connectedness and discuss a possible solution to this problem.

Tuesday, March 7, 2017

4:00 pm in 131 English Building,Tuesday, March 7, 2017

#### A variant of Gromov's H\"older equivalence problem for small step Carnot groups

###### Derek Jung   [email] (UIUC Math)

Abstract: This is the second part of a talk I gave last semester in the Graduate Geometry/Topology Seminar. A Carnot group is a Lie group that may be identified with its Lie algebra via the exponential map. This allows one to view a Carnot group as both a sub-Riemannian manifold and a geodesic metric space. It is then natural to ask the following general question: When are two Carnot groups equivalent? In this spirit, Gromov studied the problem of considering for which $k$ and $\alpha$ there exists a locally $\alpha$-H\"older homeomorphism $f:\mathbb{R}^k\to G$. Very little is known about this problem, even for the Heisenberg groups. By tweaking the class of H\"older maps, I will discuss a variant of Gromov's problem for Carnot groups of step at most three. This talk is based on a recently submitted paper. Some knowledge of differential geometry and Lie groups will be helpful.

Friday, March 17, 2017

4:00 pm in 241 Altgeld Hall,Friday, March 17, 2017

#### A 50-minute peek into the quasi-world

###### Matthew Romney (UIUC Math)

Abstract: Quasiconformal geometry is the dominant research area which evolved from complex analysis in the 20th century and remains active today. This talk will give a friendly overview to the subject, from its roots in the classical Riemann mapping theorem and Liouville theorem on conformal mappings, to some of its compelling applications in other fields, including complex dynamics and geometric group theory.

Friday, March 31, 2017

4:00 pm in 241 Altgeld Hall,Friday, March 31, 2017

#### Exotic limit sets of geodesics in Teichmuller space

###### Sarah Mousley (UIUC Math)

Abstract: In 1975, Masur proved that the Teichmuller space of a surface of genus at least 2 is not Gromov hyperbolic. Since then, many have explored to what extent Teichmuller space has features of negative curvature. In a Gromov hyperbolic space, a geodesic ray converges to a unique point in the hierarchically hyperbolic space (HHS) boundary. We will present our result that a geodesic ray in Teichmuller space does not necessarily converge to a unique point in the HHS boundary of Teichmuller space. In fact, the limit set of a ray can be almost anything allowed by topology. The goal of this talk is not to prove the result, but rather to give necessary background to understand the statement. In particular, we will not assume knowledge of Teichmuller theory or HHS structures.

Friday, April 7, 2017

4:00 pm in 241 Altgeld Hall,Friday, April 7, 2017

#### Stable Phenomena in Algebraic Topology

###### William Balderrama (UIUC Math)

Abstract: A phenomenon might be called stable if it happens the same way in every dimension. For example, if $C_\bullet$ is a chain complex, then $H_\ast C_\bullet = H_{\ast+1}C_{\bullet+1}$: taking homology'' is done the same in every dimension. In some cases, a construction might not be stable, but can be stabilized. For example, if $M$ is a smooth closed manifold, choice of distinct embeddings $i,j\colon M\rightarrow \mathbb{R}^n$ give rise to possibly nonisomorphic choices of normal bundles $N_iM$ and $N_jM$. However, we can stabilize this by adding trivial bundles: $N_iM\oplus k \simeq N_jM \oplus k$ for sufficiently large $k$, leading to the notion of the stable normal bundle. In this talk, I will introduce this notion of stability, and propose spectra, the main objects in stable homotopy theory, as a good way for dealing with it.

Friday, April 14, 2017

4:00 pm in 241 Altgeld Hall,Friday, April 14, 2017

#### Net and Filter Convergence Spaces

###### Chris Gartland (UIUC Math)

Abstract: A net or filter convergence space is a set together with a collection of data that axiomatizes the notion of convergence to an element of that set. In this sense, convergence spaces generalize topological spaces. More specifically, we will define the (equivalent) categories of net and filter convergence spaces and show that they contain the category of topological spaces (Top) as a full subcategory. We'll highlight some of the advantages these categories have over Top, especially in relation to Tychonoff's theorem. This talk is based off a series of blog posts by Jean Goubault-Larrecq, http://projects.lsv.ens-cachan.fr/topology/?page_id=785.

Friday, April 21, 2017

4:00 pm in 241 Altgeld Hall,Friday, April 21, 2017

#### It’s hard being positive: symmetric functions and Hilbert schemes

###### Joshua Wen (UIUC Math)

Abstract: Macdonald polynomials are a remarkable basis of $q,t$-deformed symmetric functions that have a tendency to show up various places in mathematics. One difficult problem in the theory was the Macdonald positivity conjecture, which roughly states that when the Macdonald polynomials are expanded in terms of the Schur function basis, the corresponding coefficients lie in $\mathbb{N}[q,t]$. This conjecture was proved by Haiman by studying the geometry of the Hilbert scheme of points on the plane. I’ll give some motivations and origins to Macdonald theory and the positivity conjecture and highlight how various structures in symmetric function theory are manifested in the algebraic geometry and topology of the Hilbert scheme. Also, if you like equivariant localization computations, then you’re in luck!

Friday, September 1, 2017

4:00 pm in 241 Altgeld Hall,Friday, September 1, 2017

#### Organizational Meeting

Abstract: This is the organizational meeting at which we schedule the talks for the semester. If you think you might be interested in giving a talk at some point, you're highly encouraged to come. As usual, there will be cookies.

Friday, September 8, 2017

4:00 pm in 241 Altgeld Hall,Friday, September 8, 2017

#### An Introduction to Classifying Spaces

###### Daniel Carmody (UIUC Math)

Abstract: In this introductory talk I'll begin by recalling the notion of a principal $G$-bundle, then I'll move to discussing how one constructs classifying spaces of such things. In the process, I'll introduce simplicial spaces and describe the relationship between simplicial spaces and topological spaces.

Friday, September 15, 2017

4:00 pm in 241 Altgeld Hall,Friday, September 15, 2017

#### From Groups to Metric Spaces: A brief introduction to coarse geometry

###### Marissa Loving (UIUC)

Abstract: In this talk we will explore the ways in which we can think of a group as a metric space and some of the notions of equivalence that can be developed to make this analogy precise. Our overarching goal will be to recognize some of the powerful tools coarse geometry makes available to us, from retrieving fine algebraic data from coarse geometric information to relating purely topological objects to purely algebraic ones. No special background will be needed as we will aim to define anything beyond what would typically be covered in Math 500.

Friday, September 22, 2017

4:00 pm in 241 Altgeld Hall,Friday, September 22, 2017